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Problem

If $ a = \langle 2, -1, 3 \rangle $ and $ b = \la…

02:51

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Problem 16 Easy Difficulty

The figure shows a vector $ a $ in the $ xy $-plane and a vector $ b $ in the direction of $ k $. Their lengths are $ \mid a \mid = 3 $ and $ \mid b \mid = 2 $.

(a) Find $ \mid a \times b \mid $.
(b) Use the right-hand rule to decide whether the components of $ a \times b $ are positive, negative, or 0.


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Related Courses

Calculus 3

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 4

The Cross Product

Related Topics

Vectors

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Lectures

Video Thumbnail

02:56

Vectors Intro

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

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11:08

Vector Basics Overview

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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Calculus: Early Transcendentals

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Top Calculus 3 Educators
Catherine Ross

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Video Thumbnail

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In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

Video Thumbnail

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Vector Basics Overview

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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